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Theorem fmptss 28279
 Description: Deduce subset relation of mapping-to function graphs from a subset relation of domains. (Contributed by Thierry Arnoux, 30-May-2020.)
Assertion
Ref Expression
fmptss
Distinct variable groups:   ,   ,
Allowed substitution hint:   ()

Proof of Theorem fmptss
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 ssel 3458 . . . 4
21anim1d 566 . . 3
32ssopab2dv 4749 . 2
4 df-mpt 4484 . 2
5 df-mpt 4484 . 2
63, 4, 53sstr4g 3505 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 370   wceq 1437   wcel 1872   wss 3436  copab 4481   cmpt 4482 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-4 1676  ax-5 1752  ax-6 1798  ax-7 1843  ax-10 1891  ax-11 1896  ax-12 1909  ax-13 2057  ax-ext 2401 This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-tru 1440  df-ex 1658  df-nf 1662  df-sb 1791  df-clab 2408  df-cleq 2414  df-clel 2417  df-nfc 2568  df-in 3443  df-ss 3450  df-opab 4483  df-mpt 4484 This theorem is referenced by:  carsgclctunlem2  29159
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